Numerical validation of a self-absorption model for plasma radiation

Abstract

This paper investigates the reliability of deducing the emissivity at the peaks of a self-reversed emission line from a simple empirical one-parameter approximation for the source function. The theory of spectral line shape formation owing to self-absorption in inhomogeneous axially symmetric plasma layers was reformulated and readily calculable expressions were obtained. In the case of self-reversed lines, the emissivity at the line maximum was calculated using different relative distributions for the densities of the absorbing and independently emitting atoms. The results were compared with those calculated using a source function described by a simple exponential law, the exponent of which is known as the inhomogeneity parameter. The obtained difference in the emissivity is less than 3%, which implies a difference in the (density-ratio) temperature between the line-levels better than 0.5%. Therefore, if the inhomogeneity parameter is known, the line emissivity can be deduced from the one-parameter approximation for the source function with reasonable accuracy. The effect of the structure of the plasma layer on the emissivity as well as the lateral dependence of the inhomogeneity parameter was also studied through numerical simulation.

Effect of spatial changes in broadening on self-absorbed lines and its impact on plasma diagnostics

“…Integrating equation (1), one then arrives at the following expression for the spectral intensity I (ν) ≡ I (ν, x 0 ) emitted along the line-of-sight at +x 0 :…”

“…Single line. In the case of a position-independent profile a simpler treatment of line self-absorption is possible using a heuristic model which is described in detail in [1]. In this model, the relative source function expressed in terms of the optical coordinate y is written in the form…”

“…The spectral intensity of a self-absorbed line is largely determined by the spatial distribution of both the source function and the line profile. The source function is closely related to the ratio of the population densities of the upper to the lower level of the emitted line and its spatial distribution characterizes the inhomogeneity of the plasma [1]. The line profile in sufficiently high-pressure and slightly ionized gas discharges, as in metal-halide arc lamps, is chiefly the result of interactions of the emitters with the surrounding neutral particles but it is also affected by electron collisions [2][3][4][5].…”

“…The theory of a symmetric self-absorbed line assuming constancy of the line profile throughout the plasma volume was developed in [1]. In this case, a rather simple treatment was shown to be possible using a heuristic model for line self-absorption.…”

“…In this case, a rather simple treatment was shown to be possible using a heuristic model for line self-absorption. A key parameter in this model is the 'inhomogeneity parameter' introduced by Cowan and Dieke [9]; details of its derivation are given in [1]. This parameter represents a one-parameter descriptor of the relative source function.…”